Course 2E01 (Frolov), Multivariable Calculus
Tutorial Sheet 6
Due: at the end of the tutorial session Tuesday/Thursday, 15/17 November 2011
1.
(a) Express rectangular coordinates in terms of spherical
Course 2E01 (Frolov), Multivariable Calculus
Tutorial Sheet 5
Due: at the end of the tutorial session Tuesday/Thursday, 1/3 November 2011
1. Consider the portion of the surface (y 1)2 + (z 1)2 = 12 th
Course 2E01 (Frolov), Multivariable Calculus
Tutorial Sheet 8
Due: at the end of the tutorial session Tuesday/Thursday, 29 November/1 December 2011
1. Consider the lamina that is the portion of the su
Course 2E01 (Frolov), Multivariable Calculus
Tutorial Sheet 7
Due: at the end of the tutorial session Tuesday/Thursday, 22/24 November 2011
1. Consider the surface that extends upward from the semicir
Course 2E01 (Frolov), Multivariable Calculus
Tutorial Sheet 10
Due: at the end of the tutorial session Tuesday/Thursday, 14/16 December 2011
1.
(a) Solve the following initial value problem by the Lap
January 25, 2010
Lecturer Dmitri Zaitsev
Hilary Term 2010
Course 2E02 2010 (SF Engineers & MSISS & MEMS)
Sheet 1
Due: at the end of the tutorial
Exercise 1
Find v + u, 2v, kuk, kvk, the dot product u
February 15, 2011
Lecturer Dmitri Zaitsev
Hilary Term 2011
Course 2E02 2011 (SF Engineers & MSISS & MEMS)
Sheet 4
Due: at the end of the tutorial
Exercise 1
Find the coordinates of the vector v with r
February 22, 2010
Lecturer Dmitri Zaitsev
Hilary Term 2011
Course 2E02 2011 (SF Engineers & MSISS & MEMS)
Sheet 5
Due: at the end of the tutorial
Exercise 1
Find the rank and the nullity of the matrix
February 1, 2011
Lecturer Dmitri Zaitsev
Hilary Term 2011
Course 2E02 2011 (SF Engineers & MSISS & MEMS)
Sheet 2
Due: at the end of the tutorial
Exercise 1
Find T (x) = Ax for the matrix A and the vec
March 22, 2010
Lecturer Dmitri Zaitsev
Hilary Term 2011
Course 2E02 2011 (SF Engineers & MSISS & MEMS)
Sheet 7
Due: at the end of the tutorial
Exercise 1
Find the characteristic polynomials of the fol
March 29, 2010
Lecturer Dmitri Zaitsev
Hilary Term 2011
Course 2E02 2011 (SF Engineers & MSISS & MEMS)
Sheet 9
Due: at the end of the tutorial
Exercise 1
Find the Fourier series of the function
f (x)
March 8, 2011
Lecturer Dmitri Zaitsev
Hilary Term 2011
Course 2E02 2011 (SF Engineers & MSISS & MEMS)
Sheet 6
Due: at the end of the tutorial
Exercise 1
Calculate the coordinates of v relative to the
February 7, 2010
Lecturer Dmitri Zaitsev
Hilary Term 2011
Course 2E02 2011 (SF Engineers & MSISS & MEMS)
Sheet 3
Due: at the end of the tutorial
Exercise 1
(i) Find parametric equations for the line s
UNIVERSITY OF DUBLIN XMA2E021
TRINITY COLLEGE
FACULTY OF ENGINEERING, MATHEMATICS
AND SCIENCE
SCHOOL OF MATHEMATICS
JF Engineers Trinity Term 2011
JF MSISS
JF MEMS
COURSE: MA2EO2 — ENGINEERING MATHEMA
Course 2E1 (Frolov), Multivariable Calculus
Tutorial Sheet 11
Due: at the end of the tutorial session Wednesday/Thursday, 4/5 February 2009
Name:
1. Find the mass of the lamina with the constant densi
Course 2E1 (Frolov), Multivariable Calculus
Tutorial Sheet 2: Solutions
Due: at the end of the tutorial session Tuesday/Thursday, 11/13 October 2011
1. Sketch the level curve z = k for the specied val
UNIVERSITY OF DUBLIN
XMA2E011
TRINITY COLLEGE
Faculty of Engineering, Mathematics
and Science
school of mathematics
SF Engineers
SF MSISS
SF MEMS
Trinity Term 2011
Module 2E011,
?, ?
Final Exam
?
9.30
Course 2E1 (Frolov), Multivariable Calculus
Tutorial Sheet 14
Due: at the end of the tutorial session Wednesday/Thursday, 25/26 February 2009
Name:
Solve the following initial value problems by the La
Course 2E1 (Frolov), Multivariable Calculus
Tutorial Sheet 15
Due: at the end of the tutorial session Wednesday/Thursday, 4/5 March 2009
Name:
1. Applying convolution, nd and sketch or plot the soluti
Course 2E1 (Frolov), Multivariable Calculus
Tutorial Sheet 12
Due: at the end of the tutorial session Wednesday/Thursday, 11/12 February 2009
Name:
1. Consider the vector eld
F(x, y, z) = (3x + 2z 2 )
Course 2E1 (Frolov), Multivariable Calculus
Tutorial Sheet 13
Due: at the end of the tutorial session Wednesday/Thursday, 18/19 February 2009
Name:
Solve the following initial value problems by the La
UNIVERSITY OF DUBLIN
XMA2E011
TRINITY COLLEGE
Faculty of Engineering, Mathematics
and Science
school of mathematics
SF Engineers
SF MSISS
SF MEMS
Trinity Term 2010
Module 2E011
Tuesday, April 27
LUCE
Course 2E1 (Frolov), Multivariable Calculus
Tutorial Sheet 3
Due: at the end of the tutorial session Tuesday/Thursday, 18/20 October 2011
1. Consider the function
y 2 + z x + 2 cos(3x 2z) ,
f (x, y, z